New York City Mayor Bill de Blasio attends the opening ceremony of the 2015 US Open on August 31, 2015 in Flushing. Photo Credit: Getty Images / Matthew Stockman

Mayor Bill de Blasio came under attack on multiple fronts Tuesday, including by former Mayor Rudy Giuliani over the shooting of the governor's aide, and former Police Commissioner Ray Kelly over the city's current NYPD policies.

The Giuliani quarrel was the latest between the 107th and 109th mayors over the city's direction under progressive Democrat de Blasio.

Police Commissioner William Bratton said the annual parade poses "probably our most problematic event in the city" and was a challenge even when Bratton was Giuliani's top cop two decades ago. Both spoke outside a House terrorism hearing where they testified.

Giuliani also kept up his criticism of de Blasio on the city's rising homelessness. He said de Blasio made "a very nasty comment about me" -- de Blasio had said Giuliani's defense of his record on homelessness is "delusional," given a 40 percent increase during his mayoralty, according to de Blasio spokeswoman Karen Hinton.

"When he reduces crime 65 percent, then he can criticize me," Giuliani said.

Earlier Tuesday, de Blasio stuck to his position blaming the homelessness problem on the 2008 recession and skyrocketing housing costs. Appearing on MSNBC's "Morning Joe," de Blasio said, "The fact is, the Great Recession led to something we hadn't seen before."

Host Joe Scarborough, who had delivered a blistering critique of the mayor last month on the issue, noted that now, "the economy's not worse; it's better."